The Double Complex of a Blow-up
Algebraic Geometry
2019-07-30 v2 Complex Variables
Differential Geometry
Abstract
We compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for 'all' cohomologies naturally associated with this complex (in particular, de-Rham, Dolbeault, Bott-Chern and Aeppli).
Keywords
Cite
@article{arxiv.1808.02882,
title = {The Double Complex of a Blow-up},
author = {Jonas Stelzig},
journal= {arXiv preprint arXiv:1808.02882},
year = {2019}
}
Comments
Inlcuded an example and discussions of product structures and extensions to singular spaces. Minor improvements throughout. Mainly following referee suggestions